As the title proclaims, the author gives an introduction to the two parts of mathematics which occur at the outset when studying mathematics at university: algebra and analysis. The central purpose of the author is not to teach the material, but rather to introduce mathematical language and the mathematical way of thinking to newcomers over several chapters. The author has succeeded in implementing his plan.

The reader is led through an easy approach to the theory of sets which nonetheless is still sufficiently deep. He learns common proof techniques and the basics of real and complex numbers. The most important results of linear algebra, group theory, sequences and series comprise the main part of the book. The large number of exercises (mostly with solutions) encourage the reader to work with the newly-learned material immediately. Further examples are available at website provided by the author. The book does not presuppose much previous knowledge, and moreover because of the nice style in which it is written, it is an excellent introduction for first-term students of mathematics.

(Translated from the German by Jorg Berns-Muller)

Geoff Smith | Introductory Mathematics: Algebra and Analysis | group pub forum